Many people experience breathing problems, which may result in difficulty sleeping, in snoring, or in other more serious conditions such as obstructive sleep apnea. One treatment for such breathing disorders involves the use of devices that are inserted into a user's mouth for extending the user's lower jaw forward. These devices open the airway (i.e., breathing passageway) more fully to allow easier breathing through the nose and mouth. Certain of these devices include upper and lower arches that are connected together using a mechanism that may be adjusted to pull the lower arch, and thus the user's lower jaw, forward to open the airway more fully. Certain devices include masks that deliver air, oxygen, or other gases to a user through their mouth and/or nasal passages.